Package elki.math.statistics
Class PolynomialRegression
- java.lang.Object
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- elki.math.statistics.MultipleLinearRegression
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- elki.math.statistics.PolynomialRegression
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public class PolynomialRegression extends MultipleLinearRegression
A polynomial fit is a specific type of multiple regression. The simple regression model (a first-order polynomial) can be trivially extended to higher orders.The regression model y = b0 + b1*x + b2*x^2 + ... + bp*x^p + e is a system of polynomial equations of order p with polynomial coefficients { b0 ... bp}. The model can be expressed using data matrix x, target double[] y and parameter double[] ?. The ith row of X and Y will contain the x and y value for the ith data sample.
The variables will be transformed in the following way: x => x1, ..., x^p => xp Then the model can be written as a multiple linear equation model: y = b0 + b1*x1 + b2*x2 + ... + bp*xp + e
- Since:
- 0.1
- Author:
- Elke Achtert
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Field Summary
Fields Modifier and Type Field Description int
p
The order of the polynom.
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Constructor Summary
Constructors Constructor Description PolynomialRegression(double[] y, double[] x, int p)
Constructor.
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Method Summary
All Methods Static Methods Instance Methods Concrete Methods Modifier and Type Method Description double
adaptedCoefficientOfDetermination()
Returns the adapted coefficient of determinationdouble
estimateY(double x)
Performs an estimation of y on the specified x value.private static double[][]
xMatrix(double[] x, int p)
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Methods inherited from class elki.math.statistics.MultipleLinearRegression
coefficientOfDetermination, estimateY, getEstimatedCoefficients, getEstimatedResiduals, getSumOfSquareResiduals, getSumOfSquaresTotal, getVariance, toString
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Method Detail
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xMatrix
private static double[][] xMatrix(double[] x, int p)
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adaptedCoefficientOfDetermination
public double adaptedCoefficientOfDetermination()
Returns the adapted coefficient of determination- Returns:
- the adapted coefficient of determination
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estimateY
public double estimateY(double x)
Performs an estimation of y on the specified x value.- Parameters:
x
- the x-value for which y is estimated- Returns:
- the estimation of y
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